<PAGE>   1

                                                                 EXHIBIT 10.6.2

                             AMENDMENT TO AGREEMENT

         THIS AMENDMENT TO AGREEMENT, made as of the 28th day of December,
1994, by and between Dillon Companies, Inc.  ("Shareholder") and E-Z Serve
Convenience Stores, Inc. ("E-Z").

                             W I T N E S S E T H :

         WHEREAS, Dillon and E-Z are parties to an Agreement dated as of
December 2, 1994, pursuant to which E-Z is to acquire the common stock of Time
Saver Stores, Inc., on the terms and conditions set forth in the Agreement; and

         WHEREAS, the parties desire to modify and amend the Agreement as set
forth below;

         NOW, THEREFORE, in consideration of the mutual agreements contained
herein, the parties agree as follows:

1.       Capitalized terms used herein shall have the meanings ascribed to them
         in the Agreement.

2.       Upon execution hereof, E-Z shall deliver to Dillon, in immediately
         available funds, the sum of Two Hundred Thousand Dollars ($200,000) as
         a non-refundable extension fee, which amount shall be credited against
         the Purchase Price, without interest, at the closing, but in no event
         (other than a failure of the transaction to close due solely to a
         default by Dillon under the Agreement, in which event the extension
         fee shall be refundable) shall such amount be refundable by Dillon, it
         being agreed by the parties that such amount shall be earned by Dillon
         on the date hereof.
<PAGE>   2
3.       Article 4 of the Agreement is hereby modified so that the term
         "December 16, 1994" in the second line thereof is changed to read
         "January 17, 1995."

4.       Section 5.1 of the Agreement is hereby modified so that the term
         "March 15, 1995" in the third line thereof is changed to read "April
         15, 1995."

5.       Section 8.1(b) of the Agreement is hereby modified so that the term
         "December 31, 1994" in the last line thereof is changed to read
         "January 17, 1995."

6.       Except as otherwise modified herein, the Agreement shall remain
         unchanged and in full force and effect.

         IN WITNESS WHEREOF, the parties hereto, intending to be legally bound,
have signed this Agreement as of the day and year first above written.

                                              DILLON COMPANIES, INC.

                                              By: /s/ FRANK J. REMAR     
                                                 -------------------------------
Attest:                                          Frank J. Remar
                                                 Senior Vice President

 /s/ HAROLD D. RYAN  
-----------------------------------
     Vice President
                                              E-Z SERVE CONVENIENCE STORES, INC.


                                              By: /s/ JOHN T. MILLER     
                                                 -------------------------------
                                                 John T. Miller 
                                                 Senior Vice President
Attest:

 /s/ H.E. LAMBERT               
-----------------------------------
     Assistant Secretary


E-Z SERVE CORPORATION joins in the execution hereof for the purposes of
consenting hereto and unconditionally guarantying the performance and
undertakings of E-Z under this Amendment
<PAGE>   3
to Agreement.

                                              E-Z SERVE CONVENIENCE STORES, INC.


                                              By: /s/ JOHN T. MILLER     
                                                 -------------------------------
                                                 John T. Miller 
                                                 Senior Vice President
Attest:

 /s/ H.E. LAMBERT               
-----------------------------------
     Assistant Secretary



STATE OF KANSAS
                                        ) SS.
COUNTY OF RENO

BE IT REMEMBERED, That on this 28th day of December 1994, before me, a Notary
Public in and for said County and State, personally appeared Frank J. Remar,
and Harold D. Ryan, Senior Vice President and Vice President, respectively, of
DILLON COMPANIES, INC., the corporation, whose name is subscribed to and which
executed the foregoing instrument, and for themselves and as such officers
respectively, and for and on behalf of the corporation, acknowledged the
signing and execution of said instrument as their free and voluntary act and
deed as such officers respectively, and the free and voluntary act and deed of
said corporation, for the uses and purposes therein mentioned.

         IN TESTIMONY WHEREOF, I have hereunto subscribed my name and affixed
my official seal, on the day and year last aforesaid.

                                       
                                           /s/ NANCY A. ROBERTS
                                          --------------------------------------
                                          Notary Public
My Commission Expires:

NOTARY PUBLIC - State of Kansas
     NANCY A. ROBERTS
   My Appt. Exp. 8/21/98


STATE OF TEXAS
                                SS.
COUNTY OF HARRIS

         BE IT REMEMBERED, That on this 28th day of December 1994, before me, a
Notary Public in and for said County and State, personally appeared John T.
Miller, and
<PAGE>   4
Harold E. Lambert, Senior Vice President and Assistant Secretary, respectively,
of E-Z Serve Convenience Stores, Inc., the corporation, whose name is
subscribed to and which executed the foregoing instrument, and for themselves
and as such officers respectively, and for and on behalf of the corporation,
acknowledged the signing and execution of said instrument as their free and
voluntary act and deed as such officers respectively, and the free and
voluntary act and deed of said corporation, for the uses and purposes therein
mentioned.

         IN TESTIMONY WHEREOF, I have hereunto subscribed my name and affixed
my Notarial seal, on the day and year last aforesaid.



                                           /s/ ANDRE MASSEY
                                          --------------------------------------
                                          Notary Public

My Commission Expires:

        ANDRE MASSEY
Notary Public, State of Texas
My Commission Expires 05-20-97

STATE OF TEXAS
                             )  SS.
COUNTY OF HARRIS

         BE IT REMEMBERED, That on this 28th day of December, 1994, before me,
a Notary Public in and for said County and State, personally appeared John T.
Miller, and Harold E. Lambert, Senior Vice President and Assistant Secretary,
respectively, of E-Z Serve Corporation, the corporation, whose name is
subscribed to and which executed the foregoing instrument, and for themselves
and as such officers respectively, and for and on behalf of the corporation,
acknowledged the signing and execution of said instrument as their free and
voluntary act and deed as such officers respectively, and the free and
voluntary act and deed of said corporation, for the uses and purposes therein
mentioned.

         IN TESTIMONY WHEREOF, I have hereunto subscribed my name and affixed
my Notarial seal, on the day and year last aforesaid.



                                           /s/ ANDRE MASSEY
                                          --------------------------------------
                                          Notary Public

My Commission Expires:

        ANDRE MASSEY
Notary Public, State of Texas
My Commission Expires 05-20-97